Petrophysical Consulting

If you have
sufficient training and experience with logs, log analysis
methods, and a year or two in the oil and gas industry, you can
probably perform the basic petrophysical analysis tasks without
learning everything on this website. In fact, many engineers,
geologists, and technical staff are given, or build for
themselves, calculator or spreadsheet programs that can do a
credible job with very minimal training.

Some of the quicklook methods embedded in these programs may be
"local" or contain assumptions that do not apply universally.
The following material provides simplified, quicklook math
suitable for programmable calculator or spreadsheet software that
covers about 95% of the world/s oil and gas reservoirs. More
detail on the methods, and alternate methods, are contained
elsewhere in this Handbook.
This presentation assumes that you have mastered the concept of
the log response equation and the visual log analysis rules
contained in other sections of this Chapter.

A spreadsheet that performs the math is available for
download and is illustrated
here.

Shale Volume

Shale is an imprecise term used to describe a
rock composed of clay, silt, and bound water. The clay type and
silt composition can vary considerably from one place to
another. These can be determined from appropriate cross plots of
PE, thorium, and potassium logs. The bound water volume varies
with clay type, depth of burial, and burial history. Some shales
have not lost as much water as others at similar depths and are
called overpressured shales. Most shales are radioactive due to
potassium and thorium, and sometimes due to uranium.

Shale volume, shown in black, can be estimated from logs in a
number of ways. The result is
the average over the interval measured by a log and is independent of the
shale distribution. Blue shading represents the effective
porosity.

Shale volume estimation is the first calculation
step in a log analysis. All other calculations depend on the
shale volume being known from this step.

STEP 1: Convert density log (gm/cc or Kg/m3) to
porosity units if a density porosity log is not available (skip
this step if density data is already in porosity units):

NOTE: The choice for KD2 must match the neutron
log units – if neutron is in Limestone units, KD2 must be 2.71
for gm/cc or 2710 for Kg/m3 log scale.

STEP 2: Calculate shale volume from the three
common methods:

3: Vshg = (GR -
GR0) / (GR100 - GR0)

4: Vshs = (SP -
SP0) / (SP100 - SP0)

5: Vshx = (PHIN
- PHID) / (PHINSH - PHIDSH)

NOTE: Trim Vsh values between 0.0 and 1.0. If too
many values fall outside this range, check the clean and shale
parameters. Do not calculate methods which fail to pass all
usage rules listed below.

STEP 3: Adjust gamma ray method for young rocks,
if needed:

8: Vshc = 1.7 -
(3.38 - (Vshg + 0.7) ^ 2) ^ 0.5

STEP 4: Take minimum of available methods:

9: Vsh = Min (Vshg,
Vshs, Vshr, Vshx, Vshc)

PARAMETERS:

GR0 = 8
to 45 GR100 = 75 to 150

SP0 = -20
to -120 SP100 = +20 to -20

PHIDSH =
-0.06 to +0.20 PHINSH = 0.15 to 0.45

All
values must be picked from logs or assumed from previous
experience.

Pore Volume

The second calculation step in a log analysis is
to find shale corrected porosity. Pore volume is the space in a
rock filled with oil, gas, or water. Total porosity includes the
bound water in the shale and is called PHIt. Effective porosity
does not include bound water, and is called PHIe. When there is
no shale, PHIe equals PHIt.

Logs read total porosity. All our analysis
methods correct for shale, so the answers from any method
presented below will give effective porosity. Some analysis
methods NEED total porosity as an intermediate step, so you may
also need to calculate it.

Raw log porosity, as presented in the field by
the service company, does NOT take into account shale or
lithology effects, so raw log readings should NEVER be used as
answers. Log analysis MUST ALWAYS be done to find the correct
porosity. All our analysis methods also account for matrix rock
(lithology), but YOU may be required to define the rock type for
some methods. Other methods will define the lithology for you.

Porosity From The Complex Lithology Density Neutron Crossplot

While there are many other porosity methods, the best method available for modern, simple, log
analysis involves the density neutron crossplot. Several
variations on the theme are common, but not all models are
recommended. A crossplot method, called the shaly sand model was
once widely used. It was found to be a poor model for any
sandstone that contained other minerals in addition to quartz.
The complex lithology model works equally well in quartz sands
as in mixtures, so it is the preferred model today. Although the
name of the method is complicated, the mathematics are not.

NORMAL CASES:

STEP 1: Shale correct the density and neutron log
data for each layer:

1: PHIdc = PHID
– (Vsh * PHIDSH)

2: PHInc = PHIN
– (Vsh * PHINSH)

PHIDSH and PHINSH are constants for each zone,
and are picked only once.

STEP 2: Check for gas crossover after shale
corrections and calculate porosity for each layer from the
correct equation:

3: IF PHInc >=
PHIdc, there is no gas crossover

4: THEN PHIxdn
= (PHInc + PHIdc) / 2

The density neutron crossplot porosity, PHIxdn,
after all corrections are applied, is called the effective
porosity, PHIe.

SPECIAL CASES:

CASE 1: IF gas is known to be present AND gas
crossover occurs after shale corrections, apply the following
gas correction:

6: IF PHInc <
PHIdc, there is gas crossover

7: THEN PHIxdn
= ((PHInc ^ 2 + PHIdc ^ 2) / 2) ^ 0.5

CASE 2: IF gas is known to be present but no
crossover occurs after shale corrections, this usually means gas
in dolomite or in a sandstone with lots of heavy minerals, apply
the following gas correction:

8: PHIx = –
PHIdc / (PHInc / 0.8 – 1) / (1 + PHIdc / (0.8 – PHInc))

9: PHIxdn =
PHIx + KD3 * (0.30 – PHIx) * (DENSMA / KD1 – KD2)

Where: KD1 = 1.00 for English units

KD1 = 1000 for
Metric units

KD2 = 2.65 for
Sandstone scale log

KD2 = 2.71 for
Limestone scale log

KD3 = 1.80 for
Sandstone scale log

KD3 = 2.00 for
Limestone scale log

CASE 3: IF rock is dolomite AND porosity is less
than 5%, use the following instead of Equation 4 or 5:

10: E = (4 -
(3.3 + 10 ^ (-5 * PHInc - 0.16))

11: PHIxdn = (E
* PHIdc + 0.754 * PHInc) / (E + 0.754)

This option can be used instead of equation 4 as
long as there is no gas crossover after shale corrections. It is
slightly more accurate, but requires a computer or preprogrammed
calculator.

Bad hole, high shale volume, and statistical
variations can cause erratic results in both very low and high
porosities. Values from any method used should be trimmed by the
following:

1: IF PHIe < 0

2: THEN PHIe =
0

3: IF PHIe >
PHIMAX * (1 - Vsh)

4: THEN PHImx =
PHIMAX * (1 - Vsh)

5: AND PHIe =
Min (PHIe, PHImx)

PARAMETERS:

PHIDSH
-0.06 - 0.15 (choose from log)

PHINSH
0.15 - 0.45 (choose from log)

Formation Water Resistivity

For simplicity, we have left out the third step
in a typical log analysis job, finding the lithology of the
rock. Refer to Chapter 13 on the main
index page for these calculations.

The fourth step in a log analysis is to determine
the water resistivity since most methods for computing water
saturation require knowledge of this value. Water resistivity
data can be sparse or overwhelming, depending on where you are
working at the moment.

RW FROM CATALOG OR LAB DATA:Catalogs and lab reports usually provide results
at 77'F (25'C) and this value must be transformed to a different
value based on the formation temperature.

STEP 1: Calculate formation temperature:

1. GRAD = (BHT
– SUFT) / BHTDEP

2: FT = SUFT +
GRAD * DEPTH

STEP 2: Calculate water resistivity at formation
temperature:

3: RW@FT = RW@TRW
* (TRW + KT1) / (FT + KT1)

Where: KT1 = 6.8 for English units

KT1 = 21.5 for
Metric units

If water salinity is reported instead of
resistivity, as may happen in reporting direct from the well
site, convert salinity to resistivity with:

4: RW@FT =
(400000 / FT1 / WS) ^ 0.88

NOTE: FT1 is in Fahrenheit

In some cases, salinity is reported in parts per
million Chloride instead of the more usual parts per million
salt (NaCl). In this situation convert Chloride to NaCl
equivalent with:

5: WS = Ccl *
1.645

To convert a downhole RW to a surface
temperature, reverse the terms in equation 3:

6: RW@SUFT = RW@FT
* (FT + KT1) / (SUFT + KT1)

Where: KT1 = 6.8 for English units

KT1 = 21.5 for
Metric units

Sometimes, it is nice to know what the resistivity log would
read in a water zone (R0). For quick look work, use the
following:
7: R0 = RW@FT ‘ (PHIe ^ 2)

RW FROM WATER ZONE:If an obvious water zone exists, calculate water
resistivity from the porosity and resistivity, as shown below.

STEP 1: Calculate water resistivity from an
obvious water zone:

1: PHIwtr = (PHIDwtr
+ PHINwtr) / 2

2: RW@FT = (PHIwtr
^ M) * R0 / A

R0 is the resistivity of a known or obvious WATER
layer and PHIwtr is the total porosity of the zone where R0 was
chosen

SPECIAL CASES:

If no obvious or known water zones exist, many
zones may be calculated with the above equations and results
scanned for low values which MIGHT be water zones. This is
called the RWa method instead of the R0 method, but the math is
the same:

1: RWai = (PHIti
^ M) * RESDi / A

Scan the list of Rwai values to find the minimum
value of Rwa in clean, moderately high porosity zones close to
the zone of interest. This Rwa value becomes RW@FT:

2: RW@FT = Min
(RWai)

The above step is the equivalent to finding RW@FT
directly from an "obvious" water zone:

3: RW@FT = (PHIwtr
^ M) * R0 / A

Note that this is the same as the Rwa equation,
but R0, the resistivity of a defined water zone replaces RESD.

PARAMETERS:

for
sandstone A = 0.62 M = 2.15 N = 2.00

for
carbonates A = 1.00 M = 2.00 N = 2.00

NOTE: A,
M, and N should be determined from special core analysis if
possible.

Water and Hydrocarbon Saturation

The fifth step in a log analysis is to find water
saturation. Water saturation is the ratio of water volume to
pore volume. Water bound to the shale is not included, so shale
corrections must be performed if shale is present. We calculate
water saturation from the effective porosity and the resistivity
log. Hydrocarbon saturation is 1 (one) minus the water
saturation.

Reservoir at initial
saturation conditions; black is hydrocarbon, white is
irreducible water (left); same
reservoir after depletion with residual oil and higher water saturation
(right).

ARCHIE METHOD:The most common saturation method was developed
by Gus Archie in 1941. It is widely used in all parts of the
world and is suitable for carbonates, clean sands, and shaly
sands where RSH is above 8 ohm-m. Where shale resistivity is
low, the Archie method will be pessimistic in shaly sands.

STEP 1: Calculate water saturation:

1: PHIt = (PHID
+ PHIN) / 2

2: Rwa = (PHIt
^ M) * RESD / A

3: SWa = (RW@FT
/ Rwa) ^ (1 / N)

The term (1/N) is usually ½ or 0.5, which
represents the square root. Hence:

3A: SWa = Sqrt (RW@FT / Rwa)

·The Archie method should only be used when Vsh <
0.20 and RSH > 8.0. If Vsh is high or RSH is low, then SWa is
too high and a shale corrected method should be used.

PARAMETERS:

for
sandstone A = 0.62 M = 2.15 N = 2.00

for
carbonates A = 1.00 M = 2.00 N = 2.00

for
fractured zones M = 1.2 to 1.7

NOTE: A,
M, and N should be determined from special core analysis if
possible.

SIMANDOUX METHOD:One of the first successful shale corrected
methods is this one, proposed by P. Simandoux in 1963. It
reduces to the Archie formula when Vsh = 0.

STEP 1: Calculate intermediate terms:

1: C = (1 – Vsh)
* A * RW@FT / (PHIe ^ M)

2: D = C * Vsh
/ (2 * RSH)

3: E = C / RESD

STEP 2: Calculate quadratic solution for water
saturation:

4: SWs = ((D ^
2 + E) ^ 0.5 – D) ^ (2 / N)

The water saturation from the Simandoux method (SWs)
is called the effective water saturation, Sw. To calculate Sxo,
replace RESD with RESS and RW@FT with RMF@FT.

USAGE RULES:

·Use Simandoux method when Vsh > 0.20 and RSH <
8.0. The dual water method may also be used and the choice is
usually a personal preference.

·The (2 / N) exponent in Equation 4 is an
approximation and works when N is near 2. More sophisticated
iterative techniques are available when N is far from 2.

DUAL WATER METHOD:Another common method, based on the cation
exchange capacity equation proposed by Waxman and Smits, is the
Schlumberger dual water model.

STEP 1: Calculate the apparent water resistivity
in shale:

0: BVWSH = (PHINSH
+ PHIDSH) / 2

1: RWSH = (BVWSH
^ M) * RSH / A

RWSH is a constant for each zone. Note that this
is the Archie equation applied to the shale zone.

STEP 2: Calculate the resistivity of the zone as
if it were 100% wet:

2: C = 1 + (BVWSH
* Vsh / PHIt * (RW@FT – RWSH) / RWSH)

3: Ro = A * RW@FT
/ (PHIt ^ M) * C

C can be larger than 1.0 if RW@FT is greater than
RWSH.

STEP 3: Calculate total and effective water
saturation:

4: SWt = (Ro /
RESD) ^ (1 / N)

5: SWd = (PHIt
* SWt – Vsh * BVWSH) / PHIe

This equation reverts to Archie when Vsh = 0.
Schlumberger uses a term called SWb, which is the bound water
expressed as a saturation, and is not the same as the SWd
calculated above.

Irreducible Water Saturation

Hydrocarbon zones with water saturation (Sw)
above irreducible saturation (SWir) will produce some water
along with hydrocarbons. This can occur in transition zones
between the oil and water legs, or after water influx into a
reservoir due to production of oil or gas.

Irreducible water saturation is a necessary value
for water cut and permeability calculations.

STEP 1: Find Buckles number from special core
analysis or from log analysis in a known clean pay zone that
produced initially with zero water cut.

1: KBUCKL =
PHIe * Sw (in a CLEAN zone that produced initially with no
water, or from core data)

The sixth step in a log analysis is to estimate
permeability and productivity. These values determine whether a
zone is commercially attractive. There are a number of methods
for calculating matrix permeability.

WYLLIE METHOD:The
general form of this equation has been used by many authors,
with various correlations between log and core data. Individual
analysts routinely calibrate their core and log data to this
equation.

STEP 1: Calculate permeability

1: PERMw =
CPERM * (PHIe ^ DPERM) / (SWir ^ EPERM)

PARAMETERS:

RESEARCHER
CPERM
DPERM EPERM

* OIL or WATER
GAS

Morris-Biggs 65000 6500
6.0 2.0

Timur
6500 650
4.5 2.0

Values of CPERM as low as 10 000 and as high as 1
000 000 have been used in the Morris - Biggs equation. It is
also called the Tixier equation.

POROSITY METHOD:

Permeability is often a semi-logarithmic function
of porosity, unfortunately with a fairly large deviation. Core
data is usually plotted to determine the equation of the best
fit line: it can be calibrated to air, absolute, maximum, or
Klinkenberg corrected permeability from core analysis,

STEP 1: Calculate permeability

1: PERMp = 10 ^
(HPERM * PHIe + JPERM)

PARAMETERS:

Sandstones Carbonates
JPERM HPERM

Very
fine grain Chalky –3.00
16

Fine
grain Cryptocrystalline- –2.50
18

Medium
grain Intercrystalline –2.20
20

Coarse
grain Sucrosic- –2.00
22

Conglomerate Fine vuggy
–1.80 24

Unconsolidated Coarse vuggy –1.50
26

Fractured Fractured
–1.00 30

The medium grain parameters approximate the
Wyllie - Rose equation. These parameters should be calibrated to
core data whenever possible.